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D₇×C₁₉×C₁₉⋊C₃ #29503136

order	15162
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

D₇×C₁₉×C₁₉⋊C₃

Splittings

Fitting, socle, Hall	C₇×C₁₉² ⋊ C₂×C₃
derived	C₇×C₁₉ ⋊ C₂×C₃×C₁₉
Hall	C₇×C₁₉×C₁₉⋊C₃ ⋊ C₂
Hall	D₇×C₁₉² ⋊ C₃
Sylow	C₁₉² ⋊ C₃×D₇
Sylow	C₇ ⋊ C₂×C₁₉×C₁₉⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₇×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉²	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 399

Conjugacy classes & character table

855 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×C₁₉×D₁₉⋊C₃, D₇×(C₁₉⋊C₃)⋊D₁₉, D₇×D₁₉×C₁₉⋊C₃, …
maximal normal subgroup of	D₇×C₁₉×D₁₉⋊C₃, D₇×(C₁₉⋊C₃)⋊D₁₉, D₇×D₁₉×C₁₉⋊C₃, …
maximal quotient of	C₁₉×Dic₇×C₁₉⋊C₃, C₂×D₇×C₁₉×C₁₉⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15162, 71);